The Floquet theory of the periodic Euler-Bernoulli equation
type: Item
instance of: scholarly article
title: The Floquet theory of the periodic Euler-Bernoulli equation
zbMATH Open document ID: 0919.34074
author: Vassilis G. Papanicolaou
author: Dimitrios Kravvaritis
published in: Journal of Differential Equations
publication date: 1999-05-02T00:00:00Z
review text: The spectrum of the eigenvalue problem \[ \bigl[a(x)u''(x)\bigr]''=\lambda\rho(x)u(x),\;-\infty<x<\infty,\tag{1} \] is studied. Here, the functions \(a(x)\) and \(\rho(x)\) are strictly positive and periodic with common period. The equality between algebraic and geometric multiplicities of the periodic and antiperiodic eigenvalues is proved. The equation (1) models transverse vibrations of a thin straight beam.
Mathematics Subject Classification ID: 34L40
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 70K40
zbMATH DE Number: 1241034
zbMATH Keywords: algebraic and geometric multiplicities
zbMATH Keywords: periodic and antiperiodic eigenvalues
zbMATH Keywords: transverse vibrations
zbMATH Keywords: thin straight beam
reviewed by: Lev A. Sakhnovich
MaRDI profile type: Publication
full work available at URL: jdeq.1998.3474
OpenAlex ID: W2054179719
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DOI: 10.1006/JDEQ.1998.3474
description: scientific article; zbMATH DE number 1241034